code: def __et_relative_bw(bins_per_octave: int) -> np.ndarray:
      """Compute the relative bandwidth coefficient for equal
      (geometric) freuqency spacing and a give number of bins
      per octave.
  
      This is a special case of the more general `relative_bandwidth`
      calculation that can be used when only a single basis frequency
      is used.
  
      Parameters
      ----------
      bins_per_octave : int
  
      Returns
      -------
      alpha : np.ndarray > 0
          Value is cast up to a 1d array to allow slicing
      """
      r = 2 ** (1 / bins_per_octave)
      return np.atleast_1d((r**2 - 1) / (r**2 + 1))
  
imports: import warnings
  import numpy
  from numba import jit
  from .None import audio
  from .intervals import interval_frequencies
  from .fft import get_fftlib
  from .convert import cqt_frequencies, note_to_hz
  from .spectrum import stft, istft
  from .pitch import estimate_tuning
  from .._cache import cache
  from ..None import filters
  from ..None import util
  from ..util.exceptions import ParameterError
  from numpy.typing import DTypeLike
  from typing import Optional, Union, Collection, List
  from .._typing import _WindowSpec, _PadMode, _FloatLike_co, _ensure_not_reachable
label_desc: Use image node_id 13 for calling a global function with example usage: __et_relative_bw(bins_per_octave) and returns: np